Non linear hyperbolic fields and waves

[1]  P. Dirac Relativistic Wave Equations , 1936 .

[2]  M. Born Quantum theory of the electromagnetic field , 1934 .

[3]  N. N. Bogoliubov,et al.  Introduction to the theory of quantized fields , 1960 .

[4]  Lev Davidovich Landau,et al.  Mécanique des fluides , 1989 .

[5]  J. Marsden,et al.  The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system, I , 1972 .

[6]  H. Tze Born duality and strings in hadrodynamics and electrodynamics , 1974 .

[7]  C. Moller,et al.  The Theory of Relativity , 1953, The Mathematical Gazette.

[8]  Tommaso Ruggeri,et al.  Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions , 1997 .

[9]  I-Shih Liu,et al.  Method of Lagrange multipliers for exploitation of the entropy principle , 1972 .

[10]  G. Rowlands,et al.  Nonlinear Waves, Solitons and Chaos , 1990 .

[11]  Tai-Ping Liu Admissible solutions of hyperbolic conservation laws , 1981 .

[12]  G. Velo,et al.  PROPAGATION AND QUANTIZATION OF RARITA--SCHWINGER WAVES IN AN EXTERNAL ELECTROMAGNETIC POTENTIAL. , 1969 .

[13]  R. E. Street,et al.  High-Speed Aerodynamics , 1956 .

[14]  A. Taub General relativistic shock waves in fluids for which pressure equals energy density , 1973 .

[15]  Guy Boillat,et al.  Onde eccezionali in mezzi iperelastici con deformazioni finite piane , 1984 .

[16]  C. Dafermos Generalized characteristics in hyperbolic systems of conservation laws , 1989 .

[17]  G. Boillat A relativistic fluid in which shock fronts are also wave surfaces , 1974 .

[18]  C. Dafermos Admissible Wave Fans in Nonlinear Hyperbolic Systems , 1989 .

[19]  P. Lax Hyperbolic systems of conservation laws II , 1957 .

[20]  A. Strumia Einstein equations, relativistic strings and Born-Infeld electrodynamics , 1995 .

[21]  C. D. Levermore,et al.  Hyperbolic conservation laws with stiff relaxation terms and entropy , 1994 .

[22]  G. Valenti,et al.  Exceptionality Condition and Linearization Procedure for a Third Order Nonlinear PDE , 1994 .

[23]  A. M. Anile,et al.  Relativistic Fluid Dynamics , 1989 .

[24]  Tommaso Ruggeri,et al.  Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics , 1981 .

[25]  John K. Hunter,et al.  Weakly nonlinear high frequency waves , 1983 .

[26]  S. Friedland,et al.  On the Crossing Rule , 1984 .

[27]  C. Rogers,et al.  The (3+1)-dimensional Monge-Ampère equation in discontinuity wave theory: Application of a reciprocal transformation , 1992 .

[28]  H. Freistühler Linear degeneracy and shock waves , 1991 .

[29]  G. Boillat Ondes asymptotiques non linéaires , 1976 .

[30]  Peter D. Lax,et al.  Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations , 1964 .

[31]  S. Pennisi A covariant and extended model for relativistic magnetofluiddynamics , 1993 .

[32]  C. Cercignani,et al.  Analysis of thermal and shear waves according to BKG kinetic model , 1985 .

[33]  Angelo Marcello Anile,et al.  Relativistic fluids and magneto-fluids , 2005 .

[34]  T. Ruggeri,et al.  On the evolution law of weak discontinuities for hyperbolic quasi-linear systems , 1979 .

[35]  Constantine M. Dafermos Quasilinear Hyperbolic Systems with Involutions , 1986 .

[36]  Albert Einstein,et al.  Briefwechsel, 1916-1955 , 1969 .

[37]  K. Friedrichs Symmetric hyperbolic linear differential equations , 1954 .

[38]  J. Mandel,et al.  Mechanical waves in solids , 1975 .

[39]  Morton E. Gurtin,et al.  Six Lectures on Modern Natural Philosophy , 1966 .

[40]  A. H. Taub,et al.  Relativistic Rankine-Hugoniot Equations , 1948 .

[41]  Ruggeri,et al.  Shock waves and second sound in a rigid heat conductor: A critical temperature for NaF and Bi. , 1990, Physical review letters.

[42]  Max Born,et al.  Foundations of the new field theory , 1934 .

[43]  W. A. Green The growth of plane discontinuities propagating into a homogeneously deformed elastic material , 1964 .

[44]  H. Arzeliès Transformation relativiste de la température et de quelques autres grandeurs thermodynamiques , 1965 .

[45]  H. Ott Lorentz-Transformation der Wärme und der Temperatur , 1963 .

[46]  P. Carbonaro Exceptional relativistic gas dynamics , 1988 .

[47]  Marco Sammartino,et al.  A thermodynamical approach to Eddington factors , 1991 .

[48]  A. Strumia Main field and symmetric-hyperbolic form of the dirac equation , 1983 .

[49]  T. Ruggeri,et al.  Symmetric form of nonlinear mechanics equations and entropy growth across a shock , 1980 .

[50]  Entropy and causality as criteria for the existence of shock waves in low temperature heat conduction , 1992 .

[51]  L. Lustman A Note on Nonbreaking Waves in Hyperelastic Materials , 1980 .

[52]  L. Seccia Shock wave propagation and admissibility criteria in a nonlinear dielectric medium , 1995 .

[53]  Science and Engineering. (Book Reviews: Non-Linear Wave Propagation. With applications to physics and magnetohydrodynamics) , 1964 .

[54]  A. Muracchini,et al.  On the symmetric conservative form of Landau's superfluid equations , 1984 .

[55]  G. Grioli On the thermodynamic potential for continuums with reversible transformations-some possible types , 1966 .

[56]  P. Lax The multiplicity of eigenvalues , 1982 .

[57]  Guy Boillat,et al.  La propagation des ondes , 1965 .

[58]  Richard Courant,et al.  Supersonic Flow And Shock Waves , 1948 .

[59]  S. K. Godunov,et al.  THE PROBLEM OF A GENERALIZED SOLUTION IN THE THEORY OF QUASILINEAR EQUATIONS AND IN GAS DYNAMICS , 1962 .

[60]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[61]  A. Muracchini,et al.  Characteristic shocks of crossing velocities in magnetohydrodynamics , 1996 .

[62]  R. Courant,et al.  THE PROPAGATION OF DISCONTINUITIES IN WAVE MOTION. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[63]  T. Ruggeri,et al.  Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks , 1979, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[64]  W. Israel Relativistic theory of shock waves , 1960, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[65]  A. Jeffrey The development of jump discontinuities in nonlinear hyperbolic systems of equations in two independent variables , 1963 .

[66]  Tosio Kato,et al.  The Cauchy problem for quasi-linear symmetric hyperbolic systems , 1975 .

[67]  G. Boillat Shock relations in nonlinear electrodynamics , 1972 .

[68]  Tai-Ping Liu Hyperbolic conservation laws with relaxation , 1987 .

[69]  G. Darmois,et al.  Théories relativistes de la gravitation et de l'électromagnétisme : relativisté générale et théories unitaires , 1955 .

[70]  F. Oliveri,et al.  Linearization of completely exceptional second order hyperbolic conservative equations , 1995 .

[71]  James Eells,et al.  PERSPECTIVES IN NONLINEARITY , 1970 .

[72]  B. S'evennec G'eom'etrie des syst`emes hyperboliques de lois de conservation , 1994 .

[73]  Non-equilibrium properties of solids obtained from second-sound measurements , 1988 .

[74]  A. M. Anile,et al.  On the mathematical structure of test relativistic magnetofluiddynamics , 1987 .

[75]  P. Germain Shock Waves, Jump Relations, and Structure , 1972 .

[76]  Constance Reid,et al.  Courant in Göttingen and New York : the story of an improbable mathematician , 1977 .

[77]  I. Müller The coldness, a universal function in thermoelastic bodies , 1971 .

[78]  G. Boillat On symmetrization of partial differential systems , 1995 .

[79]  Gabriel Nagy,et al.  The behavior of hyperbolic heat equations' solutions near their parabolic limits , 1994 .

[80]  W. Heisenberg,et al.  Folgerungen aus der Diracschen Theorie des Positrons , 1936 .

[81]  G. Boillat Sur l'équation générale de Monge-Ampère d'ordre supérieur , 1992 .

[82]  J. Smoller Shock Waves and Reaction-Diffusion Equations , 1983 .

[83]  Guy Boillat,et al.  Nonlinear Electrodynamics: Lagrangians and Equations of Motion , 1970 .

[84]  P. Lax Shock Waves and Entropy , 1971 .

[85]  A. Strumia A detailed study of entropy jump across shock waves in relativistic fluid dynamics , 1986 .

[86]  P. Lax The Initial Value Problem for Nonlinear Hyperbolic Equations in Two Independent Variables , 1954 .

[87]  G. Boillat Sur l'équation générale de Monge-Ampère à plusieurs variables , 1991 .

[88]  Constantine M. Dafermos,et al.  The Riemann problem for certain classes of hyperbolic systems of conservation laws , 1976 .

[89]  Peter D. Lax,et al.  Asymptotic solutions of oscillatory initial value problems , 1957 .

[90]  É. Goursat,et al.  Cours d'analyse mathématíque , 1919 .

[91]  Guy Boillat,et al.  Sopra l'iperbolicità dei sistemi con vincoli e considerazioni sul superfluido e la magnetoidrodinamica , 1985 .

[92]  P. Lax Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves , 1987 .

[93]  Peter Salamon,et al.  Advances in thermodynamics , 1990 .

[94]  Alan Jeffrey,et al.  Quasilinear hyperbolic systems and waves , 1976 .

[95]  R. Courant,et al.  Methods of Mathematical Physics , 1962 .

[96]  Barbara Lee Keyfitz,et al.  A system of non-strictly hyperbolic conservation laws arising in elasticity theory , 1980 .

[97]  G. Boillat Exact plane-wave solution of Born-Infeld electrodynamics , 1972 .

[98]  P. Lax,et al.  Systems of conservation equations with a convex extension. , 1971, Proceedings of the National Academy of Sciences of the United States of America.

[99]  Harold M. Edwards,et al.  Courant in Göttingen and New York: By Constance Reid. New York, Heidelberg, Berlin (Springer-Verlag). 1976. 314 pp , 1977 .

[100]  A. Jeffrey,et al.  Formation of shock waves in hyperelastic solids , 1974 .

[101]  L. Brun Ondes de Choc Finies Dans les Solides Elastiques , 1975 .

[102]  J. H. Olsen,et al.  Large-amplitude unsteady flow in liquid-filled elastic tubes , 1967, Journal of Fluid Mechanics.

[103]  G. Boillat Covariant disturbances and exceptional waves , 1973 .